Within the context of probability-based sampling from a finite population, a number of schemes have been studied to maximize or minimize the overlap between two sample selections while maintaining the required probabilities of selection for each. For example, in redesigning an in-person survey, it may be desirable to overlap the sampling of primary sampling units between the designs. Optimum solutions in general require mathematically and computationally complex approaches, but Ohlsson proposed simpler methods involving permanent random numbers applicable in some situations. Although not optimal, the methods are easily implemented and typically realize much of the gain achieved by the optimal solution. Ernst extended Ohlsson’s methods for sequential methods such as Durbin/Brewer method, by a probabilistically correct retrospective assignment of permanent random numbers. This paper presents an extension of the Ernst approach when the first sample was selected by drawing more than one unit per stratum systematically and illustrates its efficiency with a simulation study.
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